Adaptive analog fountain for wireless channels

In this paper, we propose an analog rateless code to achieve high spectral-efficient adaptive transmission and increase the system throughput in AWGN channels. In the proposed analog rateless coding scheme, each coded symbol is generated from a number of information bits that are selected uniformly at random and multiplied by some real values obtained randomly from a predetermined probability distribution function, called weight distribution. The analog rateless codes can be described by a weighted bipartite graph. However, unlike the conventional bipartite graph, where the combining coefficients are the binary symbols, the combining coefficients in the weighted bipartite graph of analog rateless codes are real numbers selected from a finite set. As a result, the conventional sum-product decoder cannot be directly applied. We have developed a simple decoding algorithm, called 2-Sum verification decoder, for the proposed analog rateless codes. Its performance is evaluated by using Sum-Or tree analysis. The code degree and weight distributions are optimized to maximize the error recovery probability of the 2-Sum verification decoder. Simulation results shows the proposed code can approach the channel capacity within one bit across a wide range of SNRs.